A test of the conjecture that G-matrices are more stable than B-matrices

The G-matrix occupies an important position in evolutionary biology both as a summary of the inheritance of quantitative traits and as an ingredient in predicting how those traits will respond to selection and drift. Consequently, the stability of G has an important bearing on the accuracy of predicted evolutionary trajectories. Furthermore, G should evolve in response to stable features of the adaptive landscape and their trajectories through time. Although the stability and evolution of G might be predicted from knowledge of selection in natural populations, most empirical comparisons of G-matrices have been made in the absence of such a priori predictions. We present a theoretical argument that within-sex G-matrices should be more stable than between-sex B-matrices because they are more powerfully exposed to multivariate stabilizing selection. We tested this conjecture by comparing estimates of B- and within-sex G-matrices among three populations of the garter snake Thamnophis elegans. Matrix comparisons using Flury's hierarchical approach revealed that within-sex G-matrices had four principal components in common (full CPC), whereas B-matrices had only a single principal component in common and eigenvalues that were more variable among populations. These results suggest that within-sex G is more stable than B, as predicted by our theoretical argument.